Solar energy conversion via internal photoemission (IPE) across a planar p-type Schottky junction is quantified for aluminum (Al) and copper (Cu) in the framework of direct transitions with non-constant matrix elements. Transition probabilities and k-resolved group velocities are obtained based on pseudo-wavefunction expansions and realistic band structures using the pseudopotential method. The k-resolved number of direct transitions, hole photocurrent density, quantum yield (QY), and the power conversion efficiency (PCE) under AM1.5G solar irradiance are subsequently calculated and analyzed. For Al, the parabolic and "parallel-band" effect along the U-W-K path significantly enhances the transition rate with final energies of holes mainly within 1.41 eV below the Fermi energy. For Cu, d-state hot holes mostly generated near the upper edge of 3d bands dominate the hole photocurrent and are weekly (strongly) dependent on the barrier height (metal film thickness). Hot holes produced in the 4s band behave just oppositely to their d-state counterparts. Non-constant matrix elements are shown to be necessary for calculations of transitions due to time-harmonic perturbation in Cu. Compared with Cu, Al-based IPE in p-type Schottky shows the highest PCE (QY) up to about 0.2673% (5.2410%) at ΦB = 0.95 eV (0.5 eV) and a film thickness of 11 nm (20 nm). It is predicted that metals with relatively dispersionless d bands (such as Cu) in most cases do not outperform metals with photon-accessible parallel bands (such as Al) in photon energy conversion using a planar p-type Schottky junction.